Dislocation-defect interactions

Up to this point we have been treating dislocations as essentially isolated line defects in solids. Obviously, dislocations in real solids coexist with other defects. The interaction of dislocations with defects is very important for the overall behavior of the solid and forms the basis for understanding several interesting phenomena. While a full discussion of these interactions is not possible in the context of the present treatment, some comments on the issue are warranted. We will consider 

As far as interactions of dislocations among themselves are concerned, these can take several forms. One example is an intersection, formed when two dislocations whose lines are at an angle meet. Depending on the type of dislocations and the angle at which they meet, this can lead to a junction (permanent lock between the two dislocations) or a jog (step on the dislocation line). The junctions make it difficult for dislocations to move past each other, hence they restrict the motion of the dislocation. We mentioned earlier how the motion of a dislocation through the crystal 

Finally, we consider the interaction of dislocations with two-dimensional obstacles such as interfaces. Most materials are composed of small crystallites whose interfaces are called grain boundaries. Interestingly, grain bovmdaries themselves can be represented as arrays of dislocations (this topic is discussed in more detail in chapter 11). Here, we will examine what happens when dislocations which exist 

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K. Van Ouytsel, R. De Batist and R. Schaller, Dislocation-defect interactions in nuclear reactor pressure-vessel steels investigated by means of internal friction , J. Alloys Comp., 2000,310,1-2,445-448. 

The vast subject of dislocations, particularly with respect to mechanical properties, will not be considered in this book, and only a few aspects of dislocations, especially interactions with point defects, will be explored. 

Edge dislocations play an important role in the strength of a metal, and screw dislocations are important in crystal growth. Dislocations also interact strongly with other defects in the crystal and can act as sources and sinks of point defects. 

At the late stage of lamella orientation, classical topological defects (dislocations and disclinations) dominate [40, 41] (Fig. 8h and Fig. 9), and their movement and annihilation can be followed in Fig. 8h-i and Fig. 9. The latter presents an example of the apparent topological defect interactions and their transformations. Displayed are two dislocations of PMMA, which have an attractive interaction due to their opposite core sign. Therefore, in the next annealing step the dislocation is shifted... 

Today there is ample evidence in catalysis that the assumption of a homogeneous surface is not valid. Thus, surface irregularities exist such as crystallographic dislocations, defects, and planes with different activity adsorbing molecules may interact with the surface and with each other several adsorption states of a species may exist on a single plane. These... 

An example of the type of data associated with solution hardening it is the mission of our models to explain was shown in fig. 8.2(a). For our present purposes, there are questions to be posed of both a qualitative and quantitative character. On the qualitative side, we would like to know how the presence of foreign atoms dissolved in the matrix can have the effect of strengthening a material. In particular, how can we reconcile what we know about point defects in solids with the elastic model of dislocation-obstacle interaction presented in section 11.6.2. From a more quantitative perspective, we are particularly interested in the question of to what extent the experimental data permit a scaling description of the hardening effect (i.e. r oc c") and in addition, to what extent statistical superposition of the presumed elastic interactions between dislocations and impurities provides for such scaling laws. 

Numerical calculations of dislocation pair interactions have been carried out for systems of particles with / [89] and LJ [90] potentials. For the potential, Fisher et al. [89] find that the elastic dislocation interaction potential is accurate for dislocation separations as small as 3 lattice spacings, while Joos and Duesbery [90] find that separations of 30 lattice spacings are necessary to reach the asymptotic elastic limit. The adequacy of the continuum elastic approximation in describing the short-range interactions between defects is thus still something of an open question, and may depend on the range of the interparticle potential. 

The concept of defects came about from crystallography. Defects are dismptions of ideal crystal lattice such as vacancies (point defects) or dislocations (linear defects). In numerous liquid crystalline phases, there is variety of defects and many of them are not observed in the solid crystals. A study of defects in liquid crystals is very important from both the academic and practical points of view [7,8]. Defects in liquid crystals are very useful for (i) identification of different phases by microscopic observation of the characteristic defects (ii) study of the elastic properties by observation of defect interactions (iii) understanding of the three-dimensional periodic structures (e.g., the blue phase in cholesterics) using a new concept of lattices of defects (iv) modelling of fundamental physical phenomena such as magnetic monopoles, interaction of quarks, etc. In the optical technology, defects usually play the detrimental role examples are defect walls in the twist nematic cells, shock instability in ferroelectric smectics, Grandjean disclinations in cholesteric cells used in dye microlasers, etc. However, more recently, defect structures find their applications in three-dimensional photonic crystals (e.g. blue phases), the bistable displays and smart memory cards. 

The operation of ceria under catalytic conditions can place the material under severe mechanical duress and therefore it is important to understand the behaviour of the material under operational conditions, such as vibration, friction, thermal cycling, etc. The mechanical properties of the material may prove pivotal. In particular, it is well known that microstructural features, such as dislocations, defects and grain boundaries, govern the mechanical properties and result in the measured mechanical strength being considerably lower than that predicted based upon the pristine, defect-free material. If one is to simulate the mechanical properties directly then atomistic models, which include all such microstructural features including their synergy of interaction, are needed. And while there are considerable efforts focused in this direction. 

For the deformation of NiAl in a soft orientation our calculations give by far the lowest Peierls barriers for the (100) 011 glide system. This glide system is also found in many experimental observations and generally accepted as the primary slip system in NiAl [18], Compared to previous atomistic modelling [6], we obtain Peierls stresses which are markedly lower. The calculated Peierls stresses (see table 1) are in the range of 40-150 MPa which is clearly at the lower end of the experimental low temperature deformation data [18]. This may either be attributed to an insufficiency of the interaction model used here or one may speculate that the low temperature deformation of NiAl is not limited by the Peierls stresses but by the interaction of the dislocations with other obstacles (possibly point defects and impurities). 

The precursor of such atomistic studies is a description of atomic interactions or, generally, knowledge of the dependence of the total energy of the system on the positions of the atoms. In principle, this is available in ab-initio total energy calculations based on the loc density functional theory (see, for example, Pettifor and Cottrell 1992). However, for extended defects, such as dislocations and interfaces, such calculations are only feasible when the number of atoms included into the calculation is well below one hundred. Hence, only very special cases can be treated in this framework and, indeed, the bulk of the dislocation and interfacial... 

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